Properties

Label 8015.2.a.l.1.61
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.61
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.76672 q^{2} +2.46366 q^{3} +5.65472 q^{4} -1.00000 q^{5} +6.81626 q^{6} -1.00000 q^{7} +10.1116 q^{8} +3.06964 q^{9} +O(q^{10})\) \(q+2.76672 q^{2} +2.46366 q^{3} +5.65472 q^{4} -1.00000 q^{5} +6.81626 q^{6} -1.00000 q^{7} +10.1116 q^{8} +3.06964 q^{9} -2.76672 q^{10} -2.78520 q^{11} +13.9313 q^{12} +3.88010 q^{13} -2.76672 q^{14} -2.46366 q^{15} +16.6665 q^{16} -4.28037 q^{17} +8.49282 q^{18} +2.70527 q^{19} -5.65472 q^{20} -2.46366 q^{21} -7.70585 q^{22} +6.92125 q^{23} +24.9116 q^{24} +1.00000 q^{25} +10.7351 q^{26} +0.171568 q^{27} -5.65472 q^{28} -8.72264 q^{29} -6.81626 q^{30} +9.05218 q^{31} +25.8882 q^{32} -6.86178 q^{33} -11.8426 q^{34} +1.00000 q^{35} +17.3580 q^{36} +11.0030 q^{37} +7.48472 q^{38} +9.55925 q^{39} -10.1116 q^{40} -12.7093 q^{41} -6.81626 q^{42} -1.77480 q^{43} -15.7495 q^{44} -3.06964 q^{45} +19.1492 q^{46} +11.5298 q^{47} +41.0606 q^{48} +1.00000 q^{49} +2.76672 q^{50} -10.5454 q^{51} +21.9409 q^{52} -3.40381 q^{53} +0.474680 q^{54} +2.78520 q^{55} -10.1116 q^{56} +6.66488 q^{57} -24.1331 q^{58} +4.06941 q^{59} -13.9313 q^{60} +11.6559 q^{61} +25.0448 q^{62} -3.06964 q^{63} +38.2924 q^{64} -3.88010 q^{65} -18.9846 q^{66} -9.21908 q^{67} -24.2043 q^{68} +17.0516 q^{69} +2.76672 q^{70} -8.15080 q^{71} +31.0389 q^{72} -7.93858 q^{73} +30.4421 q^{74} +2.46366 q^{75} +15.2976 q^{76} +2.78520 q^{77} +26.4477 q^{78} -9.55960 q^{79} -16.6665 q^{80} -8.78623 q^{81} -35.1631 q^{82} -2.97998 q^{83} -13.9313 q^{84} +4.28037 q^{85} -4.91038 q^{86} -21.4897 q^{87} -28.1628 q^{88} +8.83996 q^{89} -8.49282 q^{90} -3.88010 q^{91} +39.1378 q^{92} +22.3015 q^{93} +31.8997 q^{94} -2.70527 q^{95} +63.7798 q^{96} -16.5622 q^{97} +2.76672 q^{98} -8.54954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.76672 1.95636 0.978182 0.207748i \(-0.0666136\pi\)
0.978182 + 0.207748i \(0.0666136\pi\)
\(3\) 2.46366 1.42240 0.711198 0.702991i \(-0.248153\pi\)
0.711198 + 0.702991i \(0.248153\pi\)
\(4\) 5.65472 2.82736
\(5\) −1.00000 −0.447214
\(6\) 6.81626 2.78273
\(7\) −1.00000 −0.377964
\(8\) 10.1116 3.57499
\(9\) 3.06964 1.02321
\(10\) −2.76672 −0.874913
\(11\) −2.78520 −0.839768 −0.419884 0.907578i \(-0.637929\pi\)
−0.419884 + 0.907578i \(0.637929\pi\)
\(12\) 13.9313 4.02163
\(13\) 3.88010 1.07614 0.538072 0.842899i \(-0.319153\pi\)
0.538072 + 0.842899i \(0.319153\pi\)
\(14\) −2.76672 −0.739436
\(15\) −2.46366 −0.636115
\(16\) 16.6665 4.16662
\(17\) −4.28037 −1.03814 −0.519071 0.854731i \(-0.673722\pi\)
−0.519071 + 0.854731i \(0.673722\pi\)
\(18\) 8.49282 2.00178
\(19\) 2.70527 0.620632 0.310316 0.950634i \(-0.399565\pi\)
0.310316 + 0.950634i \(0.399565\pi\)
\(20\) −5.65472 −1.26443
\(21\) −2.46366 −0.537616
\(22\) −7.70585 −1.64289
\(23\) 6.92125 1.44318 0.721591 0.692320i \(-0.243411\pi\)
0.721591 + 0.692320i \(0.243411\pi\)
\(24\) 24.9116 5.08505
\(25\) 1.00000 0.200000
\(26\) 10.7351 2.10533
\(27\) 0.171568 0.0330183
\(28\) −5.65472 −1.06864
\(29\) −8.72264 −1.61975 −0.809877 0.586599i \(-0.800466\pi\)
−0.809877 + 0.586599i \(0.800466\pi\)
\(30\) −6.81626 −1.24447
\(31\) 9.05218 1.62582 0.812910 0.582390i \(-0.197882\pi\)
0.812910 + 0.582390i \(0.197882\pi\)
\(32\) 25.8882 4.57643
\(33\) −6.86178 −1.19448
\(34\) −11.8426 −2.03098
\(35\) 1.00000 0.169031
\(36\) 17.3580 2.89299
\(37\) 11.0030 1.80888 0.904440 0.426601i \(-0.140289\pi\)
0.904440 + 0.426601i \(0.140289\pi\)
\(38\) 7.48472 1.21418
\(39\) 9.55925 1.53071
\(40\) −10.1116 −1.59878
\(41\) −12.7093 −1.98486 −0.992431 0.122805i \(-0.960811\pi\)
−0.992431 + 0.122805i \(0.960811\pi\)
\(42\) −6.81626 −1.05177
\(43\) −1.77480 −0.270655 −0.135327 0.990801i \(-0.543209\pi\)
−0.135327 + 0.990801i \(0.543209\pi\)
\(44\) −15.7495 −2.37433
\(45\) −3.06964 −0.457595
\(46\) 19.1492 2.82339
\(47\) 11.5298 1.68180 0.840898 0.541193i \(-0.182027\pi\)
0.840898 + 0.541193i \(0.182027\pi\)
\(48\) 41.0606 5.92658
\(49\) 1.00000 0.142857
\(50\) 2.76672 0.391273
\(51\) −10.5454 −1.47665
\(52\) 21.9409 3.04265
\(53\) −3.40381 −0.467550 −0.233775 0.972291i \(-0.575108\pi\)
−0.233775 + 0.972291i \(0.575108\pi\)
\(54\) 0.474680 0.0645958
\(55\) 2.78520 0.375556
\(56\) −10.1116 −1.35122
\(57\) 6.66488 0.882784
\(58\) −24.1331 −3.16883
\(59\) 4.06941 0.529791 0.264896 0.964277i \(-0.414662\pi\)
0.264896 + 0.964277i \(0.414662\pi\)
\(60\) −13.9313 −1.79853
\(61\) 11.6559 1.49238 0.746190 0.665734i \(-0.231881\pi\)
0.746190 + 0.665734i \(0.231881\pi\)
\(62\) 25.0448 3.18070
\(63\) −3.06964 −0.386738
\(64\) 38.2924 4.78655
\(65\) −3.88010 −0.481267
\(66\) −18.9846 −2.33684
\(67\) −9.21908 −1.12629 −0.563145 0.826358i \(-0.690409\pi\)
−0.563145 + 0.826358i \(0.690409\pi\)
\(68\) −24.2043 −2.93520
\(69\) 17.0516 2.05278
\(70\) 2.76672 0.330686
\(71\) −8.15080 −0.967322 −0.483661 0.875255i \(-0.660693\pi\)
−0.483661 + 0.875255i \(0.660693\pi\)
\(72\) 31.0389 3.65797
\(73\) −7.93858 −0.929141 −0.464570 0.885536i \(-0.653791\pi\)
−0.464570 + 0.885536i \(0.653791\pi\)
\(74\) 30.4421 3.53883
\(75\) 2.46366 0.284479
\(76\) 15.2976 1.75475
\(77\) 2.78520 0.317402
\(78\) 26.4477 2.99462
\(79\) −9.55960 −1.07554 −0.537769 0.843092i \(-0.680733\pi\)
−0.537769 + 0.843092i \(0.680733\pi\)
\(80\) −16.6665 −1.86337
\(81\) −8.78623 −0.976248
\(82\) −35.1631 −3.88311
\(83\) −2.97998 −0.327096 −0.163548 0.986535i \(-0.552294\pi\)
−0.163548 + 0.986535i \(0.552294\pi\)
\(84\) −13.9313 −1.52003
\(85\) 4.28037 0.464271
\(86\) −4.91038 −0.529499
\(87\) −21.4897 −2.30393
\(88\) −28.1628 −3.00216
\(89\) 8.83996 0.937034 0.468517 0.883455i \(-0.344789\pi\)
0.468517 + 0.883455i \(0.344789\pi\)
\(90\) −8.49282 −0.895222
\(91\) −3.88010 −0.406745
\(92\) 39.1378 4.08040
\(93\) 22.3015 2.31256
\(94\) 31.8997 3.29021
\(95\) −2.70527 −0.277555
\(96\) 63.7798 6.50950
\(97\) −16.5622 −1.68164 −0.840818 0.541318i \(-0.817926\pi\)
−0.840818 + 0.541318i \(0.817926\pi\)
\(98\) 2.76672 0.279481
\(99\) −8.54954 −0.859262
\(100\) 5.65472 0.565472
\(101\) −3.94900 −0.392940 −0.196470 0.980510i \(-0.562948\pi\)
−0.196470 + 0.980510i \(0.562948\pi\)
\(102\) −29.1761 −2.88887
\(103\) 17.0324 1.67825 0.839126 0.543937i \(-0.183067\pi\)
0.839126 + 0.543937i \(0.183067\pi\)
\(104\) 39.2339 3.84720
\(105\) 2.46366 0.240429
\(106\) −9.41739 −0.914697
\(107\) 5.11239 0.494233 0.247117 0.968986i \(-0.420517\pi\)
0.247117 + 0.968986i \(0.420517\pi\)
\(108\) 0.970169 0.0933546
\(109\) −3.60978 −0.345754 −0.172877 0.984943i \(-0.555306\pi\)
−0.172877 + 0.984943i \(0.555306\pi\)
\(110\) 7.70585 0.734724
\(111\) 27.1077 2.57294
\(112\) −16.6665 −1.57483
\(113\) −4.59166 −0.431947 −0.215973 0.976399i \(-0.569292\pi\)
−0.215973 + 0.976399i \(0.569292\pi\)
\(114\) 18.4398 1.72705
\(115\) −6.92125 −0.645410
\(116\) −49.3241 −4.57963
\(117\) 11.9105 1.10113
\(118\) 11.2589 1.03647
\(119\) 4.28037 0.392381
\(120\) −24.9116 −2.27410
\(121\) −3.24269 −0.294790
\(122\) 32.2484 2.91964
\(123\) −31.3115 −2.82326
\(124\) 51.1876 4.59678
\(125\) −1.00000 −0.0894427
\(126\) −8.49282 −0.756601
\(127\) 3.89538 0.345659 0.172829 0.984952i \(-0.444709\pi\)
0.172829 + 0.984952i \(0.444709\pi\)
\(128\) 54.1679 4.78781
\(129\) −4.37252 −0.384979
\(130\) −10.7351 −0.941533
\(131\) −6.57928 −0.574834 −0.287417 0.957806i \(-0.592797\pi\)
−0.287417 + 0.957806i \(0.592797\pi\)
\(132\) −38.8015 −3.37724
\(133\) −2.70527 −0.234577
\(134\) −25.5066 −2.20343
\(135\) −0.171568 −0.0147662
\(136\) −43.2813 −3.71134
\(137\) −15.2407 −1.30210 −0.651048 0.759036i \(-0.725671\pi\)
−0.651048 + 0.759036i \(0.725671\pi\)
\(138\) 47.1771 4.01598
\(139\) 6.80209 0.576946 0.288473 0.957488i \(-0.406852\pi\)
0.288473 + 0.957488i \(0.406852\pi\)
\(140\) 5.65472 0.477911
\(141\) 28.4056 2.39218
\(142\) −22.5510 −1.89243
\(143\) −10.8068 −0.903712
\(144\) 51.1600 4.26334
\(145\) 8.72264 0.724376
\(146\) −21.9638 −1.81774
\(147\) 2.46366 0.203200
\(148\) 62.2188 5.11436
\(149\) −10.9390 −0.896155 −0.448077 0.893995i \(-0.647891\pi\)
−0.448077 + 0.893995i \(0.647891\pi\)
\(150\) 6.81626 0.556545
\(151\) −9.05777 −0.737111 −0.368556 0.929606i \(-0.620148\pi\)
−0.368556 + 0.929606i \(0.620148\pi\)
\(152\) 27.3546 2.21875
\(153\) −13.1392 −1.06224
\(154\) 7.70585 0.620955
\(155\) −9.05218 −0.727088
\(156\) 54.0549 4.32786
\(157\) −21.7165 −1.73317 −0.866584 0.499031i \(-0.833689\pi\)
−0.866584 + 0.499031i \(0.833689\pi\)
\(158\) −26.4487 −2.10415
\(159\) −8.38585 −0.665041
\(160\) −25.8882 −2.04664
\(161\) −6.92125 −0.545471
\(162\) −24.3090 −1.90990
\(163\) −3.33544 −0.261252 −0.130626 0.991432i \(-0.541699\pi\)
−0.130626 + 0.991432i \(0.541699\pi\)
\(164\) −71.8677 −5.61192
\(165\) 6.86178 0.534189
\(166\) −8.24477 −0.639918
\(167\) −4.89072 −0.378456 −0.189228 0.981933i \(-0.560598\pi\)
−0.189228 + 0.981933i \(0.560598\pi\)
\(168\) −24.9116 −1.92197
\(169\) 2.05514 0.158088
\(170\) 11.8426 0.908284
\(171\) 8.30420 0.635038
\(172\) −10.0360 −0.765239
\(173\) −6.13092 −0.466125 −0.233063 0.972462i \(-0.574875\pi\)
−0.233063 + 0.972462i \(0.574875\pi\)
\(174\) −59.4558 −4.50733
\(175\) −1.00000 −0.0755929
\(176\) −46.4193 −3.49899
\(177\) 10.0256 0.753574
\(178\) 24.4577 1.83318
\(179\) 18.0566 1.34962 0.674808 0.737994i \(-0.264227\pi\)
0.674808 + 0.737994i \(0.264227\pi\)
\(180\) −17.3580 −1.29379
\(181\) −6.85899 −0.509825 −0.254912 0.966964i \(-0.582047\pi\)
−0.254912 + 0.966964i \(0.582047\pi\)
\(182\) −10.7351 −0.795741
\(183\) 28.7161 2.12276
\(184\) 69.9849 5.15935
\(185\) −11.0030 −0.808956
\(186\) 61.7020 4.52421
\(187\) 11.9217 0.871799
\(188\) 65.1979 4.75505
\(189\) −0.171568 −0.0124797
\(190\) −7.48472 −0.542998
\(191\) −12.0769 −0.873857 −0.436928 0.899496i \(-0.643934\pi\)
−0.436928 + 0.899496i \(0.643934\pi\)
\(192\) 94.3397 6.80838
\(193\) 5.91986 0.426121 0.213061 0.977039i \(-0.431657\pi\)
0.213061 + 0.977039i \(0.431657\pi\)
\(194\) −45.8229 −3.28989
\(195\) −9.55925 −0.684552
\(196\) 5.65472 0.403909
\(197\) −11.6607 −0.830789 −0.415394 0.909641i \(-0.636356\pi\)
−0.415394 + 0.909641i \(0.636356\pi\)
\(198\) −23.6542 −1.68103
\(199\) 17.4871 1.23963 0.619813 0.784750i \(-0.287209\pi\)
0.619813 + 0.784750i \(0.287209\pi\)
\(200\) 10.1116 0.714997
\(201\) −22.7127 −1.60203
\(202\) −10.9258 −0.768735
\(203\) 8.72264 0.612210
\(204\) −59.6313 −4.17503
\(205\) 12.7093 0.887657
\(206\) 47.1238 3.28327
\(207\) 21.2458 1.47668
\(208\) 64.6675 4.48388
\(209\) −7.53471 −0.521186
\(210\) 6.81626 0.470367
\(211\) −6.26379 −0.431217 −0.215608 0.976480i \(-0.569173\pi\)
−0.215608 + 0.976480i \(0.569173\pi\)
\(212\) −19.2476 −1.32193
\(213\) −20.0808 −1.37592
\(214\) 14.1445 0.966900
\(215\) 1.77480 0.121041
\(216\) 1.73482 0.118040
\(217\) −9.05218 −0.614502
\(218\) −9.98724 −0.676421
\(219\) −19.5580 −1.32161
\(220\) 15.7495 1.06183
\(221\) −16.6082 −1.11719
\(222\) 74.9992 5.03362
\(223\) 3.39706 0.227484 0.113742 0.993510i \(-0.463716\pi\)
0.113742 + 0.993510i \(0.463716\pi\)
\(224\) −25.8882 −1.72973
\(225\) 3.06964 0.204643
\(226\) −12.7038 −0.845046
\(227\) −2.15517 −0.143044 −0.0715218 0.997439i \(-0.522786\pi\)
−0.0715218 + 0.997439i \(0.522786\pi\)
\(228\) 37.6880 2.49595
\(229\) 1.00000 0.0660819
\(230\) −19.1492 −1.26266
\(231\) 6.86178 0.451472
\(232\) −88.1998 −5.79060
\(233\) −10.3177 −0.675938 −0.337969 0.941157i \(-0.609740\pi\)
−0.337969 + 0.941157i \(0.609740\pi\)
\(234\) 32.9530 2.15420
\(235\) −11.5298 −0.752122
\(236\) 23.0114 1.49791
\(237\) −23.5516 −1.52984
\(238\) 11.8426 0.767640
\(239\) 13.7291 0.888064 0.444032 0.896011i \(-0.353548\pi\)
0.444032 + 0.896011i \(0.353548\pi\)
\(240\) −41.0606 −2.65045
\(241\) −17.0265 −1.09677 −0.548387 0.836225i \(-0.684758\pi\)
−0.548387 + 0.836225i \(0.684758\pi\)
\(242\) −8.97160 −0.576716
\(243\) −22.1610 −1.42163
\(244\) 65.9106 4.21950
\(245\) −1.00000 −0.0638877
\(246\) −86.6300 −5.52333
\(247\) 10.4967 0.667889
\(248\) 91.5319 5.81228
\(249\) −7.34168 −0.465260
\(250\) −2.76672 −0.174983
\(251\) −15.4408 −0.974613 −0.487307 0.873231i \(-0.662021\pi\)
−0.487307 + 0.873231i \(0.662021\pi\)
\(252\) −17.3580 −1.09345
\(253\) −19.2770 −1.21194
\(254\) 10.7774 0.676235
\(255\) 10.5454 0.660378
\(256\) 73.2824 4.58015
\(257\) 0.0234149 0.00146058 0.000730290 1.00000i \(-0.499768\pi\)
0.000730290 1.00000i \(0.499768\pi\)
\(258\) −12.0975 −0.753158
\(259\) −11.0030 −0.683692
\(260\) −21.9409 −1.36072
\(261\) −26.7754 −1.65735
\(262\) −18.2030 −1.12459
\(263\) −15.2066 −0.937681 −0.468841 0.883283i \(-0.655328\pi\)
−0.468841 + 0.883283i \(0.655328\pi\)
\(264\) −69.3836 −4.27026
\(265\) 3.40381 0.209095
\(266\) −7.48472 −0.458917
\(267\) 21.7787 1.33283
\(268\) −52.1313 −3.18443
\(269\) 1.93604 0.118042 0.0590211 0.998257i \(-0.481202\pi\)
0.0590211 + 0.998257i \(0.481202\pi\)
\(270\) −0.474680 −0.0288881
\(271\) 23.0187 1.39828 0.699142 0.714983i \(-0.253565\pi\)
0.699142 + 0.714983i \(0.253565\pi\)
\(272\) −71.3386 −4.32554
\(273\) −9.55925 −0.578552
\(274\) −42.1666 −2.54738
\(275\) −2.78520 −0.167954
\(276\) 96.4224 5.80394
\(277\) 27.2538 1.63752 0.818760 0.574136i \(-0.194662\pi\)
0.818760 + 0.574136i \(0.194662\pi\)
\(278\) 18.8195 1.12872
\(279\) 27.7869 1.66356
\(280\) 10.1116 0.604283
\(281\) 26.3117 1.56962 0.784812 0.619734i \(-0.212760\pi\)
0.784812 + 0.619734i \(0.212760\pi\)
\(282\) 78.5902 4.67998
\(283\) −16.5230 −0.982192 −0.491096 0.871105i \(-0.663404\pi\)
−0.491096 + 0.871105i \(0.663404\pi\)
\(284\) −46.0905 −2.73497
\(285\) −6.66488 −0.394793
\(286\) −29.8994 −1.76799
\(287\) 12.7093 0.750207
\(288\) 79.4675 4.68266
\(289\) 1.32156 0.0777391
\(290\) 24.1331 1.41714
\(291\) −40.8037 −2.39195
\(292\) −44.8905 −2.62702
\(293\) −13.8816 −0.810973 −0.405487 0.914101i \(-0.632898\pi\)
−0.405487 + 0.914101i \(0.632898\pi\)
\(294\) 6.81626 0.397532
\(295\) −4.06941 −0.236930
\(296\) 111.258 6.46672
\(297\) −0.477850 −0.0277277
\(298\) −30.2650 −1.75321
\(299\) 26.8551 1.55307
\(300\) 13.9313 0.804326
\(301\) 1.77480 0.102298
\(302\) −25.0603 −1.44206
\(303\) −9.72902 −0.558917
\(304\) 45.0873 2.58593
\(305\) −11.6559 −0.667412
\(306\) −36.3524 −2.07813
\(307\) 13.1992 0.753319 0.376659 0.926352i \(-0.377073\pi\)
0.376659 + 0.926352i \(0.377073\pi\)
\(308\) 15.7495 0.897412
\(309\) 41.9621 2.38714
\(310\) −25.0448 −1.42245
\(311\) 28.8564 1.63630 0.818148 0.575008i \(-0.195001\pi\)
0.818148 + 0.575008i \(0.195001\pi\)
\(312\) 96.6592 5.47225
\(313\) 2.52541 0.142744 0.0713722 0.997450i \(-0.477262\pi\)
0.0713722 + 0.997450i \(0.477262\pi\)
\(314\) −60.0835 −3.39071
\(315\) 3.06964 0.172955
\(316\) −54.0569 −3.04094
\(317\) 7.30718 0.410412 0.205206 0.978719i \(-0.434214\pi\)
0.205206 + 0.978719i \(0.434214\pi\)
\(318\) −23.2013 −1.30106
\(319\) 24.2943 1.36022
\(320\) −38.2924 −2.14061
\(321\) 12.5952 0.702996
\(322\) −19.1492 −1.06714
\(323\) −11.5796 −0.644304
\(324\) −49.6837 −2.76021
\(325\) 3.88010 0.215229
\(326\) −9.22821 −0.511103
\(327\) −8.89328 −0.491800
\(328\) −128.511 −7.09585
\(329\) −11.5298 −0.635659
\(330\) 18.9846 1.04507
\(331\) 23.2382 1.27729 0.638643 0.769503i \(-0.279496\pi\)
0.638643 + 0.769503i \(0.279496\pi\)
\(332\) −16.8510 −0.924818
\(333\) 33.7752 1.85087
\(334\) −13.5312 −0.740397
\(335\) 9.21908 0.503692
\(336\) −41.0606 −2.24004
\(337\) −13.8003 −0.751752 −0.375876 0.926670i \(-0.622658\pi\)
−0.375876 + 0.926670i \(0.622658\pi\)
\(338\) 5.68599 0.309277
\(339\) −11.3123 −0.614400
\(340\) 24.2043 1.31266
\(341\) −25.2121 −1.36531
\(342\) 22.9754 1.24237
\(343\) −1.00000 −0.0539949
\(344\) −17.9461 −0.967587
\(345\) −17.0516 −0.918030
\(346\) −16.9625 −0.911911
\(347\) −0.938045 −0.0503569 −0.0251784 0.999683i \(-0.508015\pi\)
−0.0251784 + 0.999683i \(0.508015\pi\)
\(348\) −121.518 −6.51406
\(349\) 14.7934 0.791874 0.395937 0.918278i \(-0.370420\pi\)
0.395937 + 0.918278i \(0.370420\pi\)
\(350\) −2.76672 −0.147887
\(351\) 0.665700 0.0355324
\(352\) −72.1037 −3.84314
\(353\) −34.8870 −1.85685 −0.928423 0.371524i \(-0.878835\pi\)
−0.928423 + 0.371524i \(0.878835\pi\)
\(354\) 27.7381 1.47427
\(355\) 8.15080 0.432600
\(356\) 49.9875 2.64933
\(357\) 10.5454 0.558121
\(358\) 49.9576 2.64034
\(359\) −16.7591 −0.884509 −0.442255 0.896890i \(-0.645821\pi\)
−0.442255 + 0.896890i \(0.645821\pi\)
\(360\) −31.0389 −1.63590
\(361\) −11.6815 −0.614817
\(362\) −18.9769 −0.997403
\(363\) −7.98889 −0.419308
\(364\) −21.9409 −1.15001
\(365\) 7.93858 0.415524
\(366\) 79.4493 4.15288
\(367\) −4.39917 −0.229635 −0.114817 0.993387i \(-0.536628\pi\)
−0.114817 + 0.993387i \(0.536628\pi\)
\(368\) 115.353 6.01318
\(369\) −39.0130 −2.03094
\(370\) −30.4421 −1.58261
\(371\) 3.40381 0.176717
\(372\) 126.109 6.53845
\(373\) 16.4329 0.850861 0.425431 0.904991i \(-0.360123\pi\)
0.425431 + 0.904991i \(0.360123\pi\)
\(374\) 32.9839 1.70556
\(375\) −2.46366 −0.127223
\(376\) 116.585 6.01240
\(377\) −33.8447 −1.74309
\(378\) −0.474680 −0.0244149
\(379\) 16.9307 0.869673 0.434837 0.900509i \(-0.356806\pi\)
0.434837 + 0.900509i \(0.356806\pi\)
\(380\) −15.2976 −0.784748
\(381\) 9.59690 0.491664
\(382\) −33.4135 −1.70958
\(383\) −18.1103 −0.925393 −0.462697 0.886517i \(-0.653118\pi\)
−0.462697 + 0.886517i \(0.653118\pi\)
\(384\) 133.452 6.81017
\(385\) −2.78520 −0.141947
\(386\) 16.3786 0.833648
\(387\) −5.44800 −0.276938
\(388\) −93.6547 −4.75459
\(389\) −11.6034 −0.588316 −0.294158 0.955757i \(-0.595039\pi\)
−0.294158 + 0.955757i \(0.595039\pi\)
\(390\) −26.4477 −1.33923
\(391\) −29.6255 −1.49823
\(392\) 10.1116 0.510712
\(393\) −16.2091 −0.817642
\(394\) −32.2618 −1.62533
\(395\) 9.55960 0.480996
\(396\) −48.3453 −2.42944
\(397\) 25.7939 1.29456 0.647281 0.762252i \(-0.275906\pi\)
0.647281 + 0.762252i \(0.275906\pi\)
\(398\) 48.3818 2.42516
\(399\) −6.66488 −0.333661
\(400\) 16.6665 0.833323
\(401\) −19.4018 −0.968879 −0.484439 0.874825i \(-0.660976\pi\)
−0.484439 + 0.874825i \(0.660976\pi\)
\(402\) −62.8396 −3.13416
\(403\) 35.1233 1.74962
\(404\) −22.3305 −1.11099
\(405\) 8.78623 0.436591
\(406\) 24.1331 1.19771
\(407\) −30.6455 −1.51904
\(408\) −106.631 −5.27901
\(409\) 34.5242 1.70711 0.853557 0.521000i \(-0.174441\pi\)
0.853557 + 0.521000i \(0.174441\pi\)
\(410\) 35.1631 1.73658
\(411\) −37.5478 −1.85210
\(412\) 96.3135 4.74503
\(413\) −4.06941 −0.200242
\(414\) 58.7810 2.88893
\(415\) 2.97998 0.146282
\(416\) 100.449 4.92490
\(417\) 16.7581 0.820646
\(418\) −20.8464 −1.01963
\(419\) 14.6639 0.716376 0.358188 0.933649i \(-0.383395\pi\)
0.358188 + 0.933649i \(0.383395\pi\)
\(420\) 13.9313 0.679780
\(421\) −26.3449 −1.28397 −0.641986 0.766716i \(-0.721889\pi\)
−0.641986 + 0.766716i \(0.721889\pi\)
\(422\) −17.3301 −0.843617
\(423\) 35.3924 1.72084
\(424\) −34.4180 −1.67148
\(425\) −4.28037 −0.207628
\(426\) −55.5580 −2.69179
\(427\) −11.6559 −0.564066
\(428\) 28.9092 1.39738
\(429\) −26.6244 −1.28544
\(430\) 4.91038 0.236799
\(431\) −27.7047 −1.33449 −0.667244 0.744839i \(-0.732526\pi\)
−0.667244 + 0.744839i \(0.732526\pi\)
\(432\) 2.85943 0.137574
\(433\) −16.9803 −0.816022 −0.408011 0.912977i \(-0.633777\pi\)
−0.408011 + 0.912977i \(0.633777\pi\)
\(434\) −25.0448 −1.20219
\(435\) 21.4897 1.03035
\(436\) −20.4123 −0.977573
\(437\) 18.7239 0.895684
\(438\) −54.1114 −2.58554
\(439\) 34.0794 1.62652 0.813260 0.581900i \(-0.197691\pi\)
0.813260 + 0.581900i \(0.197691\pi\)
\(440\) 28.1628 1.34261
\(441\) 3.06964 0.146173
\(442\) −45.9503 −2.18563
\(443\) 0.461355 0.0219196 0.0109598 0.999940i \(-0.496511\pi\)
0.0109598 + 0.999940i \(0.496511\pi\)
\(444\) 153.286 7.27465
\(445\) −8.83996 −0.419054
\(446\) 9.39871 0.445042
\(447\) −26.9499 −1.27469
\(448\) −38.2924 −1.80915
\(449\) −8.12986 −0.383672 −0.191836 0.981427i \(-0.561444\pi\)
−0.191836 + 0.981427i \(0.561444\pi\)
\(450\) 8.49282 0.400356
\(451\) 35.3979 1.66682
\(452\) −25.9646 −1.22127
\(453\) −22.3153 −1.04846
\(454\) −5.96274 −0.279845
\(455\) 3.88010 0.181902
\(456\) 67.3925 3.15594
\(457\) −25.6777 −1.20115 −0.600576 0.799567i \(-0.705062\pi\)
−0.600576 + 0.799567i \(0.705062\pi\)
\(458\) 2.76672 0.129280
\(459\) −0.734374 −0.0342776
\(460\) −39.1378 −1.82481
\(461\) −18.4427 −0.858960 −0.429480 0.903076i \(-0.641303\pi\)
−0.429480 + 0.903076i \(0.641303\pi\)
\(462\) 18.9846 0.883244
\(463\) 35.5395 1.65166 0.825831 0.563918i \(-0.190707\pi\)
0.825831 + 0.563918i \(0.190707\pi\)
\(464\) −145.376 −6.74889
\(465\) −22.3015 −1.03421
\(466\) −28.5463 −1.32238
\(467\) 38.3440 1.77435 0.887175 0.461433i \(-0.152665\pi\)
0.887175 + 0.461433i \(0.152665\pi\)
\(468\) 67.3506 3.11328
\(469\) 9.21908 0.425697
\(470\) −31.8997 −1.47143
\(471\) −53.5023 −2.46525
\(472\) 41.1482 1.89400
\(473\) 4.94317 0.227287
\(474\) −65.1607 −2.99293
\(475\) 2.70527 0.124126
\(476\) 24.2043 1.10940
\(477\) −10.4485 −0.478403
\(478\) 37.9846 1.73738
\(479\) 17.0528 0.779162 0.389581 0.920992i \(-0.372620\pi\)
0.389581 + 0.920992i \(0.372620\pi\)
\(480\) −63.7798 −2.91114
\(481\) 42.6926 1.94662
\(482\) −47.1075 −2.14569
\(483\) −17.0516 −0.775877
\(484\) −18.3365 −0.833477
\(485\) 16.5622 0.752051
\(486\) −61.3133 −2.78123
\(487\) 9.20575 0.417152 0.208576 0.978006i \(-0.433117\pi\)
0.208576 + 0.978006i \(0.433117\pi\)
\(488\) 117.859 5.33524
\(489\) −8.21740 −0.371603
\(490\) −2.76672 −0.124988
\(491\) 39.8874 1.80009 0.900046 0.435794i \(-0.143533\pi\)
0.900046 + 0.435794i \(0.143533\pi\)
\(492\) −177.058 −7.98238
\(493\) 37.3361 1.68154
\(494\) 29.0414 1.30664
\(495\) 8.54954 0.384273
\(496\) 150.868 6.77416
\(497\) 8.15080 0.365613
\(498\) −20.3123 −0.910218
\(499\) −38.3664 −1.71752 −0.858758 0.512382i \(-0.828763\pi\)
−0.858758 + 0.512382i \(0.828763\pi\)
\(500\) −5.65472 −0.252887
\(501\) −12.0491 −0.538314
\(502\) −42.7203 −1.90670
\(503\) −0.943900 −0.0420864 −0.0210432 0.999779i \(-0.506699\pi\)
−0.0210432 + 0.999779i \(0.506699\pi\)
\(504\) −31.0389 −1.38258
\(505\) 3.94900 0.175728
\(506\) −53.3341 −2.37099
\(507\) 5.06317 0.224863
\(508\) 22.0273 0.977303
\(509\) 19.5367 0.865950 0.432975 0.901406i \(-0.357464\pi\)
0.432975 + 0.901406i \(0.357464\pi\)
\(510\) 29.1761 1.29194
\(511\) 7.93858 0.351182
\(512\) 94.4159 4.17263
\(513\) 0.464138 0.0204922
\(514\) 0.0647823 0.00285743
\(515\) −17.0324 −0.750537
\(516\) −24.7254 −1.08847
\(517\) −32.1128 −1.41232
\(518\) −30.4421 −1.33755
\(519\) −15.1045 −0.663015
\(520\) −39.2339 −1.72052
\(521\) 15.8024 0.692317 0.346159 0.938176i \(-0.387486\pi\)
0.346159 + 0.938176i \(0.387486\pi\)
\(522\) −74.0799 −3.24239
\(523\) 16.3958 0.716939 0.358470 0.933541i \(-0.383299\pi\)
0.358470 + 0.933541i \(0.383299\pi\)
\(524\) −37.2040 −1.62526
\(525\) −2.46366 −0.107523
\(526\) −42.0725 −1.83445
\(527\) −38.7467 −1.68783
\(528\) −114.362 −4.97695
\(529\) 24.9038 1.08277
\(530\) 9.41739 0.409065
\(531\) 12.4916 0.542090
\(532\) −15.2976 −0.663233
\(533\) −49.3134 −2.13600
\(534\) 60.2555 2.60751
\(535\) −5.11239 −0.221028
\(536\) −93.2195 −4.02647
\(537\) 44.4854 1.91969
\(538\) 5.35646 0.230934
\(539\) −2.78520 −0.119967
\(540\) −0.970169 −0.0417494
\(541\) 40.4855 1.74061 0.870304 0.492514i \(-0.163922\pi\)
0.870304 + 0.492514i \(0.163922\pi\)
\(542\) 63.6861 2.73555
\(543\) −16.8982 −0.725173
\(544\) −110.811 −4.75099
\(545\) 3.60978 0.154626
\(546\) −26.4477 −1.13186
\(547\) −11.5683 −0.494626 −0.247313 0.968936i \(-0.579548\pi\)
−0.247313 + 0.968936i \(0.579548\pi\)
\(548\) −86.1817 −3.68150
\(549\) 35.7793 1.52702
\(550\) −7.70585 −0.328578
\(551\) −23.5971 −1.00527
\(552\) 172.419 7.33865
\(553\) 9.55960 0.406515
\(554\) 75.4034 3.20359
\(555\) −27.1077 −1.15066
\(556\) 38.4640 1.63124
\(557\) 5.09219 0.215763 0.107881 0.994164i \(-0.465593\pi\)
0.107881 + 0.994164i \(0.465593\pi\)
\(558\) 76.8786 3.25453
\(559\) −6.88640 −0.291264
\(560\) 16.6665 0.704287
\(561\) 29.3710 1.24004
\(562\) 72.7970 3.07076
\(563\) −8.79425 −0.370634 −0.185317 0.982679i \(-0.559331\pi\)
−0.185317 + 0.982679i \(0.559331\pi\)
\(564\) 160.626 6.76356
\(565\) 4.59166 0.193173
\(566\) −45.7146 −1.92153
\(567\) 8.78623 0.368987
\(568\) −82.4176 −3.45816
\(569\) 11.9491 0.500930 0.250465 0.968126i \(-0.419416\pi\)
0.250465 + 0.968126i \(0.419416\pi\)
\(570\) −18.4398 −0.772359
\(571\) 1.20752 0.0505333 0.0252666 0.999681i \(-0.491957\pi\)
0.0252666 + 0.999681i \(0.491957\pi\)
\(572\) −61.1096 −2.55512
\(573\) −29.7535 −1.24297
\(574\) 35.1631 1.46768
\(575\) 6.92125 0.288636
\(576\) 117.544 4.89766
\(577\) 35.5590 1.48034 0.740171 0.672419i \(-0.234745\pi\)
0.740171 + 0.672419i \(0.234745\pi\)
\(578\) 3.65640 0.152086
\(579\) 14.5846 0.606113
\(580\) 49.3241 2.04807
\(581\) 2.97998 0.123631
\(582\) −112.892 −4.67953
\(583\) 9.48028 0.392633
\(584\) −80.2717 −3.32167
\(585\) −11.9105 −0.492438
\(586\) −38.4065 −1.58656
\(587\) 11.5101 0.475074 0.237537 0.971378i \(-0.423660\pi\)
0.237537 + 0.971378i \(0.423660\pi\)
\(588\) 13.9313 0.574519
\(589\) 24.4886 1.00903
\(590\) −11.2589 −0.463521
\(591\) −28.7280 −1.18171
\(592\) 183.381 7.53690
\(593\) 11.1301 0.457057 0.228529 0.973537i \(-0.426609\pi\)
0.228529 + 0.973537i \(0.426609\pi\)
\(594\) −1.32208 −0.0542454
\(595\) −4.28037 −0.175478
\(596\) −61.8568 −2.53375
\(597\) 43.0823 1.76324
\(598\) 74.3005 3.03838
\(599\) −4.49294 −0.183576 −0.0917882 0.995779i \(-0.529258\pi\)
−0.0917882 + 0.995779i \(0.529258\pi\)
\(600\) 24.9116 1.01701
\(601\) 1.20991 0.0493533 0.0246766 0.999695i \(-0.492144\pi\)
0.0246766 + 0.999695i \(0.492144\pi\)
\(602\) 4.91038 0.200132
\(603\) −28.2992 −1.15243
\(604\) −51.2192 −2.08408
\(605\) 3.24269 0.131834
\(606\) −26.9174 −1.09345
\(607\) −19.6635 −0.798116 −0.399058 0.916926i \(-0.630663\pi\)
−0.399058 + 0.916926i \(0.630663\pi\)
\(608\) 70.0346 2.84028
\(609\) 21.4897 0.870805
\(610\) −32.2484 −1.30570
\(611\) 44.7368 1.80986
\(612\) −74.2985 −3.00334
\(613\) 12.1251 0.489727 0.244863 0.969558i \(-0.421257\pi\)
0.244863 + 0.969558i \(0.421257\pi\)
\(614\) 36.5185 1.47377
\(615\) 31.3115 1.26260
\(616\) 28.1628 1.13471
\(617\) 9.86111 0.396993 0.198497 0.980102i \(-0.436394\pi\)
0.198497 + 0.980102i \(0.436394\pi\)
\(618\) 116.097 4.67012
\(619\) −13.2257 −0.531584 −0.265792 0.964030i \(-0.585633\pi\)
−0.265792 + 0.964030i \(0.585633\pi\)
\(620\) −51.1876 −2.05574
\(621\) 1.18747 0.0476513
\(622\) 79.8374 3.20119
\(623\) −8.83996 −0.354165
\(624\) 159.319 6.37786
\(625\) 1.00000 0.0400000
\(626\) 6.98708 0.279260
\(627\) −18.5630 −0.741334
\(628\) −122.801 −4.90030
\(629\) −47.0968 −1.87787
\(630\) 8.49282 0.338362
\(631\) −36.3077 −1.44539 −0.722694 0.691168i \(-0.757096\pi\)
−0.722694 + 0.691168i \(0.757096\pi\)
\(632\) −96.6627 −3.84504
\(633\) −15.4319 −0.613362
\(634\) 20.2169 0.802916
\(635\) −3.89538 −0.154583
\(636\) −47.4197 −1.88031
\(637\) 3.88010 0.153735
\(638\) 67.2154 2.66108
\(639\) −25.0200 −0.989777
\(640\) −54.1679 −2.14117
\(641\) −36.0976 −1.42577 −0.712884 0.701282i \(-0.752611\pi\)
−0.712884 + 0.701282i \(0.752611\pi\)
\(642\) 34.8474 1.37532
\(643\) −17.4409 −0.687802 −0.343901 0.939006i \(-0.611748\pi\)
−0.343901 + 0.939006i \(0.611748\pi\)
\(644\) −39.1378 −1.54224
\(645\) 4.37252 0.172168
\(646\) −32.0374 −1.26049
\(647\) −29.4329 −1.15713 −0.578563 0.815638i \(-0.696386\pi\)
−0.578563 + 0.815638i \(0.696386\pi\)
\(648\) −88.8428 −3.49007
\(649\) −11.3341 −0.444902
\(650\) 10.7351 0.421066
\(651\) −22.3015 −0.874066
\(652\) −18.8610 −0.738653
\(653\) −30.2109 −1.18225 −0.591123 0.806582i \(-0.701315\pi\)
−0.591123 + 0.806582i \(0.701315\pi\)
\(654\) −24.6052 −0.962140
\(655\) 6.57928 0.257074
\(656\) −211.819 −8.27015
\(657\) −24.3686 −0.950709
\(658\) −31.8997 −1.24358
\(659\) −37.2550 −1.45125 −0.725625 0.688090i \(-0.758449\pi\)
−0.725625 + 0.688090i \(0.758449\pi\)
\(660\) 38.8015 1.51035
\(661\) 48.2225 1.87564 0.937818 0.347126i \(-0.112843\pi\)
0.937818 + 0.347126i \(0.112843\pi\)
\(662\) 64.2935 2.49884
\(663\) −40.9171 −1.58909
\(664\) −30.1324 −1.16936
\(665\) 2.70527 0.104906
\(666\) 93.4464 3.62098
\(667\) −60.3716 −2.33760
\(668\) −27.6557 −1.07003
\(669\) 8.36922 0.323573
\(670\) 25.5066 0.985405
\(671\) −32.4638 −1.25325
\(672\) −63.7798 −2.46036
\(673\) 6.49244 0.250265 0.125133 0.992140i \(-0.460064\pi\)
0.125133 + 0.992140i \(0.460064\pi\)
\(674\) −38.1816 −1.47070
\(675\) 0.171568 0.00660365
\(676\) 11.6212 0.446971
\(677\) 22.5654 0.867260 0.433630 0.901091i \(-0.357232\pi\)
0.433630 + 0.901091i \(0.357232\pi\)
\(678\) −31.2979 −1.20199
\(679\) 16.5622 0.635599
\(680\) 43.2813 1.65976
\(681\) −5.30961 −0.203465
\(682\) −69.7547 −2.67105
\(683\) 8.32378 0.318501 0.159250 0.987238i \(-0.449092\pi\)
0.159250 + 0.987238i \(0.449092\pi\)
\(684\) 46.9580 1.79548
\(685\) 15.2407 0.582315
\(686\) −2.76672 −0.105634
\(687\) 2.46366 0.0939946
\(688\) −29.5797 −1.12771
\(689\) −13.2071 −0.503151
\(690\) −47.1771 −1.79600
\(691\) 3.78947 0.144158 0.0720790 0.997399i \(-0.477037\pi\)
0.0720790 + 0.997399i \(0.477037\pi\)
\(692\) −34.6687 −1.31791
\(693\) 8.54954 0.324770
\(694\) −2.59530 −0.0985164
\(695\) −6.80209 −0.258018
\(696\) −217.295 −8.23653
\(697\) 54.4006 2.06057
\(698\) 40.9292 1.54919
\(699\) −25.4194 −0.961452
\(700\) −5.65472 −0.213728
\(701\) 18.1619 0.685966 0.342983 0.939342i \(-0.388563\pi\)
0.342983 + 0.939342i \(0.388563\pi\)
\(702\) 1.84180 0.0695144
\(703\) 29.7660 1.12265
\(704\) −106.652 −4.01959
\(705\) −28.4056 −1.06982
\(706\) −96.5224 −3.63267
\(707\) 3.94900 0.148518
\(708\) 56.6923 2.13063
\(709\) −30.7243 −1.15388 −0.576938 0.816788i \(-0.695752\pi\)
−0.576938 + 0.816788i \(0.695752\pi\)
\(710\) 22.5510 0.846323
\(711\) −29.3445 −1.10051
\(712\) 89.3860 3.34988
\(713\) 62.6524 2.34635
\(714\) 29.1761 1.09189
\(715\) 10.8068 0.404152
\(716\) 102.105 3.81585
\(717\) 33.8240 1.26318
\(718\) −46.3676 −1.73042
\(719\) 37.1924 1.38704 0.693520 0.720437i \(-0.256059\pi\)
0.693520 + 0.720437i \(0.256059\pi\)
\(720\) −51.1600 −1.90662
\(721\) −17.0324 −0.634320
\(722\) −32.3194 −1.20281
\(723\) −41.9476 −1.56005
\(724\) −38.7857 −1.44146
\(725\) −8.72264 −0.323951
\(726\) −22.1030 −0.820319
\(727\) 52.6578 1.95297 0.976485 0.215585i \(-0.0691659\pi\)
0.976485 + 0.215585i \(0.0691659\pi\)
\(728\) −39.2339 −1.45411
\(729\) −28.2386 −1.04587
\(730\) 21.9638 0.812917
\(731\) 7.59681 0.280978
\(732\) 162.382 6.00180
\(733\) −10.0745 −0.372110 −0.186055 0.982539i \(-0.559570\pi\)
−0.186055 + 0.982539i \(0.559570\pi\)
\(734\) −12.1713 −0.449249
\(735\) −2.46366 −0.0908736
\(736\) 179.179 6.60462
\(737\) 25.6769 0.945822
\(738\) −107.938 −3.97325
\(739\) −15.2860 −0.562305 −0.281152 0.959663i \(-0.590717\pi\)
−0.281152 + 0.959663i \(0.590717\pi\)
\(740\) −62.2188 −2.28721
\(741\) 25.8604 0.950004
\(742\) 9.41739 0.345723
\(743\) 23.6187 0.866485 0.433243 0.901277i \(-0.357369\pi\)
0.433243 + 0.901277i \(0.357369\pi\)
\(744\) 225.504 8.26737
\(745\) 10.9390 0.400773
\(746\) 45.4651 1.66459
\(747\) −9.14747 −0.334689
\(748\) 67.4137 2.46489
\(749\) −5.11239 −0.186803
\(750\) −6.81626 −0.248895
\(751\) −20.5806 −0.750998 −0.375499 0.926823i \(-0.622529\pi\)
−0.375499 + 0.926823i \(0.622529\pi\)
\(752\) 192.161 7.00740
\(753\) −38.0409 −1.38629
\(754\) −93.6387 −3.41012
\(755\) 9.05777 0.329646
\(756\) −0.970169 −0.0352847
\(757\) 30.0680 1.09284 0.546420 0.837511i \(-0.315990\pi\)
0.546420 + 0.837511i \(0.315990\pi\)
\(758\) 46.8426 1.70140
\(759\) −47.4922 −1.72386
\(760\) −27.3546 −0.992255
\(761\) 34.7817 1.26084 0.630419 0.776255i \(-0.282883\pi\)
0.630419 + 0.776255i \(0.282883\pi\)
\(762\) 26.5519 0.961874
\(763\) 3.60978 0.130683
\(764\) −68.2918 −2.47071
\(765\) 13.1392 0.475048
\(766\) −50.1061 −1.81041
\(767\) 15.7897 0.570132
\(768\) 180.543 6.51479
\(769\) −23.7711 −0.857209 −0.428605 0.903492i \(-0.640995\pi\)
−0.428605 + 0.903492i \(0.640995\pi\)
\(770\) −7.70585 −0.277699
\(771\) 0.0576864 0.00207752
\(772\) 33.4752 1.20480
\(773\) 15.3469 0.551991 0.275995 0.961159i \(-0.410993\pi\)
0.275995 + 0.961159i \(0.410993\pi\)
\(774\) −15.0731 −0.541791
\(775\) 9.05218 0.325164
\(776\) −167.470 −6.01183
\(777\) −27.1077 −0.972482
\(778\) −32.1033 −1.15096
\(779\) −34.3821 −1.23187
\(780\) −54.0549 −1.93548
\(781\) 22.7016 0.812326
\(782\) −81.9655 −2.93108
\(783\) −1.49653 −0.0534815
\(784\) 16.6665 0.595231
\(785\) 21.7165 0.775097
\(786\) −44.8461 −1.59961
\(787\) 27.4856 0.979755 0.489878 0.871791i \(-0.337041\pi\)
0.489878 + 0.871791i \(0.337041\pi\)
\(788\) −65.9379 −2.34894
\(789\) −37.4640 −1.33375
\(790\) 26.4487 0.941003
\(791\) 4.59166 0.163261
\(792\) −86.4495 −3.07185
\(793\) 45.2258 1.60602
\(794\) 71.3646 2.53263
\(795\) 8.38585 0.297415
\(796\) 98.8846 3.50487
\(797\) 47.8270 1.69412 0.847060 0.531497i \(-0.178370\pi\)
0.847060 + 0.531497i \(0.178370\pi\)
\(798\) −18.4398 −0.652763
\(799\) −49.3519 −1.74594
\(800\) 25.8882 0.915286
\(801\) 27.1355 0.958785
\(802\) −53.6793 −1.89548
\(803\) 22.1105 0.780262
\(804\) −128.434 −4.52952
\(805\) 6.92125 0.243942
\(806\) 97.1763 3.42289
\(807\) 4.76974 0.167903
\(808\) −39.9307 −1.40476
\(809\) −13.7959 −0.485039 −0.242519 0.970147i \(-0.577974\pi\)
−0.242519 + 0.970147i \(0.577974\pi\)
\(810\) 24.3090 0.854132
\(811\) −26.7332 −0.938728 −0.469364 0.883005i \(-0.655517\pi\)
−0.469364 + 0.883005i \(0.655517\pi\)
\(812\) 49.3241 1.73094
\(813\) 56.7102 1.98892
\(814\) −84.7873 −2.97179
\(815\) 3.33544 0.116835
\(816\) −175.754 −6.15263
\(817\) −4.80132 −0.167977
\(818\) 95.5188 3.33974
\(819\) −11.9105 −0.416186
\(820\) 71.8677 2.50973
\(821\) −6.92473 −0.241675 −0.120837 0.992672i \(-0.538558\pi\)
−0.120837 + 0.992672i \(0.538558\pi\)
\(822\) −103.884 −3.62338
\(823\) 50.6906 1.76696 0.883482 0.468466i \(-0.155193\pi\)
0.883482 + 0.468466i \(0.155193\pi\)
\(824\) 172.225 5.99973
\(825\) −6.86178 −0.238897
\(826\) −11.2589 −0.391747
\(827\) −8.29416 −0.288416 −0.144208 0.989547i \(-0.546063\pi\)
−0.144208 + 0.989547i \(0.546063\pi\)
\(828\) 120.139 4.17512
\(829\) −9.57303 −0.332485 −0.166243 0.986085i \(-0.553163\pi\)
−0.166243 + 0.986085i \(0.553163\pi\)
\(830\) 8.24477 0.286180
\(831\) 67.1441 2.32920
\(832\) 148.578 5.15102
\(833\) −4.28037 −0.148306
\(834\) 46.3648 1.60548
\(835\) 4.89072 0.169250
\(836\) −42.6067 −1.47358
\(837\) 1.55306 0.0536817
\(838\) 40.5707 1.40149
\(839\) 46.0697 1.59050 0.795251 0.606281i \(-0.207339\pi\)
0.795251 + 0.606281i \(0.207339\pi\)
\(840\) 24.9116 0.859530
\(841\) 47.0845 1.62360
\(842\) −72.8889 −2.51192
\(843\) 64.8231 2.23263
\(844\) −35.4200 −1.21921
\(845\) −2.05514 −0.0706990
\(846\) 97.9207 3.36658
\(847\) 3.24269 0.111420
\(848\) −56.7295 −1.94810
\(849\) −40.7072 −1.39707
\(850\) −11.8426 −0.406197
\(851\) 76.1545 2.61054
\(852\) −113.552 −3.89021
\(853\) −55.2158 −1.89055 −0.945276 0.326272i \(-0.894208\pi\)
−0.945276 + 0.326272i \(0.894208\pi\)
\(854\) −32.2484 −1.10352
\(855\) −8.30420 −0.283998
\(856\) 51.6944 1.76688
\(857\) −54.8924 −1.87509 −0.937545 0.347865i \(-0.886907\pi\)
−0.937545 + 0.347865i \(0.886907\pi\)
\(858\) −73.6621 −2.51478
\(859\) −44.1250 −1.50553 −0.752763 0.658291i \(-0.771279\pi\)
−0.752763 + 0.658291i \(0.771279\pi\)
\(860\) 10.0360 0.342225
\(861\) 31.3115 1.06709
\(862\) −76.6510 −2.61074
\(863\) −1.04695 −0.0356387 −0.0178193 0.999841i \(-0.505672\pi\)
−0.0178193 + 0.999841i \(0.505672\pi\)
\(864\) 4.44159 0.151106
\(865\) 6.13092 0.208458
\(866\) −46.9797 −1.59644
\(867\) 3.25589 0.110576
\(868\) −51.1876 −1.73742
\(869\) 26.6253 0.903203
\(870\) 59.4558 2.01574
\(871\) −35.7709 −1.21205
\(872\) −36.5006 −1.23607
\(873\) −50.8400 −1.72067
\(874\) 51.8036 1.75228
\(875\) 1.00000 0.0338062
\(876\) −110.595 −3.73666
\(877\) −41.5066 −1.40158 −0.700789 0.713368i \(-0.747169\pi\)
−0.700789 + 0.713368i \(0.747169\pi\)
\(878\) 94.2880 3.18207
\(879\) −34.1997 −1.15353
\(880\) 46.4193 1.56480
\(881\) −30.6281 −1.03189 −0.515944 0.856622i \(-0.672559\pi\)
−0.515944 + 0.856622i \(0.672559\pi\)
\(882\) 8.49282 0.285968
\(883\) 37.8262 1.27295 0.636476 0.771296i \(-0.280391\pi\)
0.636476 + 0.771296i \(0.280391\pi\)
\(884\) −93.9150 −3.15870
\(885\) −10.0256 −0.337008
\(886\) 1.27644 0.0428828
\(887\) 1.49090 0.0500596 0.0250298 0.999687i \(-0.492032\pi\)
0.0250298 + 0.999687i \(0.492032\pi\)
\(888\) 274.101 9.19824
\(889\) −3.89538 −0.130647
\(890\) −24.4577 −0.819823
\(891\) 24.4714 0.819822
\(892\) 19.2095 0.643180
\(893\) 31.1913 1.04378
\(894\) −74.5628 −2.49375
\(895\) −18.0566 −0.603566
\(896\) −54.1679 −1.80962
\(897\) 66.1620 2.20909
\(898\) −22.4930 −0.750602
\(899\) −78.9589 −2.63343
\(900\) 17.3580 0.578599
\(901\) 14.5696 0.485383
\(902\) 97.9360 3.26091
\(903\) 4.37252 0.145508
\(904\) −46.4290 −1.54420
\(905\) 6.85899 0.228001
\(906\) −61.7401 −2.05118
\(907\) −45.0913 −1.49723 −0.748615 0.663005i \(-0.769281\pi\)
−0.748615 + 0.663005i \(0.769281\pi\)
\(908\) −12.1869 −0.404436
\(909\) −12.1220 −0.402062
\(910\) 10.7351 0.355866
\(911\) 29.4533 0.975830 0.487915 0.872891i \(-0.337758\pi\)
0.487915 + 0.872891i \(0.337758\pi\)
\(912\) 111.080 3.67822
\(913\) 8.29983 0.274684
\(914\) −71.0430 −2.34989
\(915\) −28.7161 −0.949325
\(916\) 5.65472 0.186837
\(917\) 6.57928 0.217267
\(918\) −2.03181 −0.0670596
\(919\) 32.0222 1.05632 0.528158 0.849146i \(-0.322883\pi\)
0.528158 + 0.849146i \(0.322883\pi\)
\(920\) −69.9849 −2.30733
\(921\) 32.5184 1.07152
\(922\) −51.0256 −1.68044
\(923\) −31.6259 −1.04098
\(924\) 38.8015 1.27648
\(925\) 11.0030 0.361776
\(926\) 98.3278 3.23125
\(927\) 52.2833 1.71721
\(928\) −225.814 −7.41269
\(929\) 39.6002 1.29924 0.649620 0.760259i \(-0.274928\pi\)
0.649620 + 0.760259i \(0.274928\pi\)
\(930\) −61.7020 −2.02329
\(931\) 2.70527 0.0886616
\(932\) −58.3440 −1.91112
\(933\) 71.0924 2.32746
\(934\) 106.087 3.47128
\(935\) −11.9217 −0.389880
\(936\) 120.434 3.93651
\(937\) −15.3496 −0.501450 −0.250725 0.968058i \(-0.580669\pi\)
−0.250725 + 0.968058i \(0.580669\pi\)
\(938\) 25.5066 0.832819
\(939\) 6.22175 0.203039
\(940\) −65.1979 −2.12652
\(941\) −14.3675 −0.468368 −0.234184 0.972192i \(-0.575242\pi\)
−0.234184 + 0.972192i \(0.575242\pi\)
\(942\) −148.026 −4.82293
\(943\) −87.9644 −2.86452
\(944\) 67.8226 2.20744
\(945\) 0.171568 0.00558110
\(946\) 13.6764 0.444657
\(947\) 18.5760 0.603638 0.301819 0.953365i \(-0.402406\pi\)
0.301819 + 0.953365i \(0.402406\pi\)
\(948\) −133.178 −4.32542
\(949\) −30.8024 −0.999890
\(950\) 7.48472 0.242836
\(951\) 18.0024 0.583769
\(952\) 43.2813 1.40276
\(953\) −42.2489 −1.36858 −0.684288 0.729212i \(-0.739887\pi\)
−0.684288 + 0.729212i \(0.739887\pi\)
\(954\) −28.9080 −0.935930
\(955\) 12.0769 0.390801
\(956\) 77.6345 2.51088
\(957\) 59.8529 1.93477
\(958\) 47.1803 1.52433
\(959\) 15.2407 0.492146
\(960\) −94.3397 −3.04480
\(961\) 50.9419 1.64329
\(962\) 118.118 3.80829
\(963\) 15.6932 0.505706
\(964\) −96.2802 −3.10098
\(965\) −5.91986 −0.190567
\(966\) −47.1771 −1.51790
\(967\) −53.2374 −1.71200 −0.856000 0.516975i \(-0.827058\pi\)
−0.856000 + 0.516975i \(0.827058\pi\)
\(968\) −32.7887 −1.05387
\(969\) −28.5281 −0.916456
\(970\) 45.8229 1.47129
\(971\) 10.9588 0.351683 0.175842 0.984418i \(-0.443735\pi\)
0.175842 + 0.984418i \(0.443735\pi\)
\(972\) −125.314 −4.01946
\(973\) −6.80209 −0.218065
\(974\) 25.4697 0.816102
\(975\) 9.55925 0.306141
\(976\) 194.262 6.21817
\(977\) 34.4869 1.10333 0.551667 0.834064i \(-0.313992\pi\)
0.551667 + 0.834064i \(0.313992\pi\)
\(978\) −22.7352 −0.726992
\(979\) −24.6210 −0.786891
\(980\) −5.65472 −0.180634
\(981\) −11.0807 −0.353780
\(982\) 110.357 3.52164
\(983\) 17.3874 0.554572 0.277286 0.960787i \(-0.410565\pi\)
0.277286 + 0.960787i \(0.410565\pi\)
\(984\) −316.609 −10.0931
\(985\) 11.6607 0.371540
\(986\) 103.299 3.28970
\(987\) −28.4056 −0.904160
\(988\) 59.3560 1.88837
\(989\) −12.2839 −0.390604
\(990\) 23.6542 0.751779
\(991\) −6.01968 −0.191221 −0.0956107 0.995419i \(-0.530480\pi\)
−0.0956107 + 0.995419i \(0.530480\pi\)
\(992\) 234.345 7.44045
\(993\) 57.2511 1.81681
\(994\) 22.5510 0.715273
\(995\) −17.4871 −0.554377
\(996\) −41.5152 −1.31546
\(997\) −28.1454 −0.891375 −0.445687 0.895189i \(-0.647041\pi\)
−0.445687 + 0.895189i \(0.647041\pi\)
\(998\) −106.149 −3.36009
\(999\) 1.88776 0.0597261
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))